Causal structure of higher curvature gravity

In this paper, we analyze the causal structure of generalized quadratic gravity (GQG) and Einsteinian cubic gravity (ECG). It is well known that gravitons in higher-curvature theories can exhibit superluminal propagation, rendering the conventional definition of causal structures based on null curves inadequate. Instead, the causal structure must be defined using the fastest propagating modes, which travel along characteristic surfaces. The superluminal propagation in higher-curvature theories has significant implications for black holes. Specifically, if the Killing horizon of a black hole is not a characteristic surface corresponding to the fastest propagating mode, the horizon can no longer function as a causal barrier. Our analysis demonstrates that GQG with a genuine fourth-order equation of motion possesses only null characteristics, implying that the horizon is a characteristic surface. Furthermore, we perform a detailed characteristic analysis of ECG. We show that while all null surfaces are characteristic surfaces in ECG, the converse is not true—there exist non-null characteristic surfaces. In particular, we identify a non-null characteristic surface in a Type N spacetime in the algebraic classification of spacetimes. Despite the existence of multiple characteristic surfaces in ECG, we establish that the black hole horizon remains a characteristic surface.